find atleast 3 solutions for the following linear equation in two variables:2x + 3y = 4​

Answer:

[tex] x = \dfrac{-\log 7}{\log 7 - \log 2} [/tex]

Step-by-step explanation:

[tex] 2^x = 7^{x + 1} [/tex]

Take the log of both sides.

[tex] \log 2^x = \log 7^{x + 1} [/tex]

Use properties of log.

[tex] x \log 2 = (x + 1) \log 7 [/tex]

[tex] x \log 2 = x \log 7 + \log 7 [/tex]

[tex] x \log 2 - x \log 7 = \log 7 [/tex]

[tex] x(\log 2 - \log 7) = \log 7 [/tex]

[tex] x = \dfrac{\log 7}{\log 2 - \log 7} [/tex]

[tex] x = \dfrac{\log 7}{-(\log 7 - \log 2)} [/tex]

[tex] x = \dfrac{-\log 7}{\log 7 - \log 2} [/tex]

Answer:

54 marbles

Step-by-step explanation:

The question is a word problem leading to a simultaneous equation

Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,

If Mary gives Sam 5 marbles, we have;

x + 5 = 2 × (y - 5)...(1)

If Sam gives Mary 4 marbles, we get;

x - 4 = y + 4...(2)

From equation (1), we get;

x + 5 = 2 × (y - 5) = 2·y - 10

x = 2·y - 10 - 5 = 2·y - 15

x = 2·y - 15...(3)

From equation (2), we have;

x - 4 = y + 4

∴ x = y + 4 + 4 = y + 8

x = y + 8...(4)

Equating the two values of 'x' in equation (3), and equation (4), we get;

2·y - 15 = y + 8

2·y - y = 8 + 15 = 23

∴ y = 23

From equation (4), we get;

x = y + 8 = 23 + 8 = 31

x = 31

The total number of marbles they have altogether = x + y

However, x + y = 23 + 31 = 54

Therefore;

The total number of marbles they have altogether = 54 marbles.

Answer:

13 + 3i

Step-by-step explanation:

I just used a app for this problem.

Answer:

[tex]13 + 3i[/tex] is the sum of the numbers

Step-by-step explanation:

[tex]13 + 3i[/tex]

[tex]15 - 6i - 2 + 9i[/tex]  → Sum

collect like terms

[tex](15 - 2) + ( - 6i + 9i) =13 + 3i[/tex]

Answer:

QR = 65.4 m

Step-by-step explanation:

a. Apply Law of Cosines to find QR:

p² = q² + r² - 2qr × Cos P

p = QR = ?

q = PR = 150 m

r = PQ = 120 m

P = 25°

Plug in the values

p² = 150² + 120² - (2)(150)(120) × Cos(25°)

p² = 22,500 + 14,400 - 36,000 × 0.9063

p² = 36,900 - 32,626.8

p² = 4,273.2

p = √4,273.2

p ≈ 65.4 m (nearest tenth)

QR = 65.4 m

Answer:

1

Step-by-step explanation:

S = {,10,11,12,13,14,15,16,17,18,19,}

n(s) = 10

P(a) = n(a) / n(s)

= 10 / 10

= 1 / 1

= 1

hope this helps.....

Answer:

x = 5±sqrt(26)

Step-by-step explanation:

x^2-10x=1

Take the coefficient of x

-10

Divide by 2

-10/2 = -5

Square it

(-5)^2 = 25

Add this to both side

x^2-10x+25=1+25

(x-5)^2 = 26

Take the square root of each side

sqrt((x-5)^2) = ±sqrt(26)

x-5 = ±sqrt(26)

Add 5 to each side

x = 5±sqrt(26)

Answer:

-0.0990195 and 10.09902

Step-by-step explanation:

To complete the square, the same value needs to be added to both sides

x^2-10x+?=1+?

To complete the square x^2-10x+25=(x-5)^2 add 25 to the expression.

x^2-10x+25=1+?

Since 25 was added to the left-side, you need to add it to the right-side as well.

x^2-10x+25=1+25

use a^2-2ab+b^2=(a-b)^2 to factor this expression.

(x-5)^2=1+25

Then add the numbers together.

(x-5)^2=26

Solve for x.

x1=-squareroot26+5

x2=squareroot26+5

therefore you have 2 solutions

x1=-squareroot26+5

=-0.0990195

and

x2=squareroot26+5

=10.09902

Answer:

She earns $0.65 per paper

Step-by-step explanation:

1. She earns $3.90 per 6 papers

2. take $3.90 and divide by 6.

3. you will get the cost per paper.

4. to check the work if you'd like then take 7.80 and divide it by 12 and again you will get $0.65 per paper.

(you don't need to find a special calculator you can use one on your phone since each dollar has 100 cents so you just need to go out to the hundredths place in a decimal or the second decimal place)

Answer:

3rd choice

Step-by-step explanation:

Similar triangles have congruent angles and proportional sides

They look similar but size may vary

Answer:

1) V

2) V

3) V

4) V

5) V

Step-by-step explanation:

answer:

[tex]{ \tt{ \cos(100x) + \frac{4}{3} = 0}} \\ { \tt{ \cos(100x) = - \frac{4}{3} }} \\ { \tt{100x = { \cos }^{ - 1} ( - \frac{4}{3} )}} \\ { \tt{invalid \: answer}}[/tex]

15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.

16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.

17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.

18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.

19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.

20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.

Hope this helps! :)

Answer:

x = -2

When we multiply a negative number with a positive number the answer is always negative.

Hope it helps:)

Answer:

Option D: (0,-5)

Step-by-step explanation:

Comparing the given points to the graph.

So, the point that will lie at the shaded area represent  solution to the linear inequality.

So, point (0,-5) is a solution to the linear inequality.

The answer is option D. (0,-5)

Note: the line y = 6x-4 is graphed using the table on the graph.

We can say 85 because we will spin it 85 times and it can happen we will not C

Not sure at all ....

Answer:

81

Step-by-step explanation:

It depends on how many different grades you have and the values of each one of them.

I don't have those things, so Ill just use average.

You'll have an 81

Answer:

The inequality is [tex]9\leq p\leq 15[/tex]

Step-by-step explanation:

The minimum number of players is 9 and the maximum number of players are 15.

let the number of players is p.

The inequality is given by

[tex]9\leq p\leq 15[/tex]

120

Step-by-step explanation:

if "1 hour is 24 muffins"

you can either use '+' or '×' to find the ans,

for example,

- 24+24+24+24+24 = 120

[formula 1]

using '+' is the longer way to solve the question

the easier way is by using '×', which will solve the question faster (with this you need to memorise the time table!^^)

- 24 × 5 = 120

[formula 2]

Both gives the same amount of ans, but only has a different way of solving it!

Answer: [tex]180\ cm^2[/tex]

Step-by-step explanation:

Given

Height of a cuboid [tex]h=45\ mm[/tex]

Volume of the cuboid is [tex]V=162\ cm^3[/tex]

End faces are square. So, assume its length to be x

[tex]\therefore x^2\times h=162\\\Rightarrow x^2\times 4.5=162\\\Rightarrow x^2=36\\\Rightarrow x=6\ cm[/tex]

Surface area of cuboid

[tex]\Rightarrow 2(lb+bh+hl)=2(6\times 6+6\times 4.5+4.5\times 6)\\\Rightarrow 2(36+27+27)\\\Rightarrow 180\ cm^2[/tex]

Answer:

(x+6)^2 + y^2 = 1 then isolate y^2  by subtracting (x +6)^2 from both sides, we get

                y^2 = 1 - (x + 6)^2

expanding the right side, we now have

                y^2 = 1-(x^2 + 12x +36)

          y^2 = 1-x^2-12x -36

          y^2 = -x^2 -12x - 35  therefore the solution is  choice A

Step-by-step explanation:

Answer:

[tex]\frac{3}{25}[/tex]

Step-by-step explanation:

          [tex]12 \% = \frac{12}{100} = \frac{3}{25}[/tex]

Answer:

3/25

Step-by-step explanation:

12 %

to remove % sign divide 12 by 100

12/100

3/25

Answer:

-9.25

Step-by-step explanation:

-5.75 - 3.5

-9.25

[tex]\implies {\blue {\boxed {\boxed {\pink {\sf { \:- 9 \frac{1}{4} (or) \:- 9.25 }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] - 5 \frac{3}{4} - 3 \frac{1}{2} [/tex]

➺[tex] \: \frac{ - 23}{4} - \frac{7}{2} [/tex]

➺[tex] \: \frac{ - 23}{4} - \frac{7 \times 2}{2 \times 2} [/tex]

➺[tex] \: \frac{ - 23 - 14}{4} [/tex]

➺[tex] \frac{ - 37}{4} [/tex]

➺[tex] \: - 9 \frac{1}{4} [/tex]

➺[tex] \: -9.25[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

166.8 feet

Step-by-step explanation:

tan = opp/adj

opp = height of tree

adj = distance

tan27 = 85/distance

distance = 85/tan27

use calculator

distance = 166.821892967937799

166.8 feet

Answer: -7y = 21

explanation:

x+y=2;3x−4y=27

Step: Solve x+y=2 for x:

x+y+−y=2+−y (Add -y to both sides)

x=−y+2

Step: Substitute −y+2 for x in 3x−4y=27:

3x−4y=27

3(−y+2)−4y=27

−7y+6=27 (Simplify both sides of the equation)

−7y+6+−6=27+−6 (Add -6 to both sides)

−7y=21 (answer)

first option

manipulate line 1 to

x = 2 - y

then substitute x in line to for the righthand side above

then solve towards y.

Answer:

2,023

Step-by-step explanation:

P(8) = 25(8)²-24(8)+615

= 1600- 192 +615

= 2,023

Answer:

p(10) = 306

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

p(x) = 3(x² - 2) + 12

p(10) is x = 10 for function p(x)

Step 2: Evaluate

Answer:

….

Step-by-step explanation:

You will need an image for that!

Answer:

1/2

Step-by-step explanation:

These two triangles are similar, so there is a scale factor. The heights and the bottom sides of each triangle are similar, figure A has a bottom length of 6, and figure B has a bottom length of 3. To get from A to B, you multiply by 1/2. So the scale factor is 1/2.